The Brother support page for the HL-2270DW can can be found here. It's actually pretty good.
Win 7 (32-bit) - will probably work for Win 10 as well, but has not been tested
Recommended setup process for the HL-2270DW:
Download and unzip (don't just view, but actually uncompress) the driver only (below)
Get the MAC address for the printer (can be found by printing the configuration page - be sure to get the wireless (BRW), not the wired (BRN) MAC address)
Assign a static IP address for the printer using the MAC address in the router
Reboot the router
Download the full installer below
Follow these instructions, using the temporary USB connection method.
Brother actually has a pile of downloads; I've aggregated them in three groups. The files are the same for Win 7 & Win 10.
Full Installer: This is the full install package, which tries to help you configure and add the printer.
Driver Only: This is really all that's needed for Tax-Aide purposes.
Brother utlities: this is a bundle of three or four distinct utilities that Brother makes available for troubleshooting and monkeying with network printers. They can come in handy, but aren't needed as a rule of thumb. Brother is a little funny about these - the utilities are mostly generic and work across Brother's entire printer line, but Brother does not update all utility downloads for all printers when they update them. I'm not sure if this is because they know something I don't, or they just don't bother to update the downloads for printers they no longer sell.